View source for Ed7

'''Ed7''' means '''Division of the Seventh Harmonic ([[7/1]]) into n equal parts'''.

== Properties ==
The seventh harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~3.9 heptataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with heptatave equivalence, this fact shapes one's musical approach dramatically.

Incidentally, one way to treat 7/1 as an equivalence is to eliminate the primes 2, 3, and 5 and use the 7:11:13:(49) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes seven [[13/7]] to get to [[11/7]] ([[tempering out]] the [[comma]] 63412811/62748517 in the 7.11.13 [[subgroup]]). This temperament yields 10, 13, 16, 19, 22, 25, and 47 note [[MOS]]. If 7/1 is too wide to be used as an equivalence, the next best option would be [[Ed11/7|equal divisions of 11/7]].

== Table of similar ETs ==

{| class="wikitable"
! ED7 !! Similar EDO !! Similar EDT !! Similar EDF
|-
| [[7ed7]] ||  || [[4edt]] || 
|-
| [[9ed7]] ||  || [[5edt]] || 
|-
| [[11ed7]] || [[4edo]] ||  || 
|-
| [[14ed7]] || [[5edo]] ||  || 
|-
| [[16ed7]] ||  || [[9edt]] || 
|-
| [[17ed7]] || [[6edo]] ||  || 
|-
| [[18ed7]] ||  || [[10edt]] || 
|-
| [[21ed7]] ||  || [[12edt]] || 
|-
| [[23ed7]] ||  || [[13edt]] || 
|-
| [[25ed7]] || [[9edo]] ||  || 
|-
| [[28ed7]] || [[10edo]] ||  || 
|-
| [[30ed7]] ||  || [[17edt]] || 
|-
| [[31ed7]] || [[11edo]] ||  || 
|-
| [[32ed7]] ||  || [[18edt]] || 
|-
| [[34ed7]] || [[12edo]] ||  || 
|-
| [[37ed7]] ||  || [[21edt]] || 
|-
| [[39ed7]] || [[14edo]] ||  || 
|-
| [[41ed7]] ||  || [[23edt]] || 
|-
| [[42ed7]] || [[15edo]] ||  || 
|-
| [[44ed7]] ||  || [[25edt]] || 
|-
| [[45ed7]] || [[16edo]] ||  || 
|-
| [[46ed7]] ||  || [[26edt]] || 
|-
| [[48ed7]] || [[17edo]] ||  || 
|-
| [[53ed7]] ||  || [[30edt]] || 
|-
| [[55ed7]] ||  || [[31edt]] || 
|-
| [[56ed7]] || [[20edo]] ||  || 
|-
| [[57ed7]] ||  || [[32edt]] || 
|-
| [[59ed7]] || [[21edo]] ||  || 
|-
| [[60ed7]] ||  || [[34edt]] || 
|-
| [[62ed7]] || [[22edo]] ||  || 
|-
| [[64ed7]] ||  || [[36edt]] || 
|-
| [[67ed7]] ||  || [[38edt]] || 
|-
| [[69ed7]] ||  || [[39edt]] || 
|-
| [[70ed7]] || [[25edo]] ||  || 
|-
| [[71ed7]] ||  || [[40edt]] || 
|-
| [[73ed7]] || [[26edo]] ||  || 
|-
| [[76ed7]] || [[27edo]] ||  || 
|-
| [[78ed7]] ||  || [[44edt]] || 
|-
| [[80ed7]] ||  || [[45edt]] || 
|-
| [[83ed7]] ||  || [[47edt]] || 
|-
| [[84ed7]] || [[30edo]] ||  || 
|-
| [[85ed7]] ||  || [[48edt]] || 
|-
| [[87ed7]] || [[31edo]] ||  || 
|-
| [[90ed7]] || [[32edo]] ||  || 
|-
| [[92ed7]] ||  || [[52edt]] || 
|-
| [[94ed7]] ||  || [[53edt]] || 
|-
| [[96ed7]] ||  ||  || [[20edf]] (& [[Carlos Gamma]])
|-
| [[98ed7]] || [[35edo]] ||  || 
|-
| [[99ed7]] ||  || [[56edt]] || 
|}

== Individual pages for ED7s == 
{| class="wikitable center-all"
|+ style=white-space:nowrap | 0…99
| [[0ed7|0]]
| [[1ed7|1]]
| [[2ed7|2]]
| [[3ed7|3]]
| [[4ed7|4]]
| [[5ed7|5]]
| [[6ed7|6]]
| [[7ed7|7]]
| [[8ed7|8]]
| [[9ed7|9]]
|-
| [[10ed7|10]]
| [[11ed7|11]]
| [[12ed7|12]]
| [[13ed7|13]]
| [[14ed7|14]]
| [[15ed7|15]]
| [[16ed7|16]]
| [[17ed7|17]]
| [[18ed7|18]]
| [[19ed7|19]]
|-
| [[20ed7|20]]
| [[21ed7|21]]
| [[22ed7|22]]
| [[23ed7|23]]
| [[24ed7|24]]
| [[25ed7|25]]
| [[26ed7|26]]
| [[27ed7|27]]
| [[28ed7|28]]
| [[29ed7|29]]
|-
| [[30ed7|30]]
| [[31ed7|31]]
| [[32ed7|32]]
| [[33ed7|33]]
| [[34ed7|34]]
| [[35ed7|35]]
| [[36ed7|36]]
| [[37ed7|37]]
| [[38ed7|38]]
| [[39ed7|39]]
|-
| [[40ed7|40]]
| [[41ed7|41]]
| [[42ed7|42]]
| [[43ed7|43]]
| [[44ed7|44]]
| [[45ed7|45]]
| [[46ed7|46]]
| [[47ed7|47]]
| [[48ed7|48]]
| [[49ed7|49]]
|-
| [[50ed7|50]]
| [[51ed7|51]]
| [[52ed7|52]]
| [[53ed7|53]]
| [[54ed7|54]]
| [[55ed7|55]]
| [[56ed7|56]]
| [[57ed7|57]]
| [[58ed7|58]]
| [[59ed7|59]]
|-
| [[60ed7|60]]
| [[61ed7|61]]
| [[62ed7|62]]
| [[63ed7|63]]
| [[64ed7|64]]
| [[65ed7|65]]
| [[66ed7|66]]
| [[67ed7|67]]
| [[68ed7|68]]
| [[69ed7|69]]
|-
| [[70ed7|70]]
| [[71ed7|71]]
| [[72ed7|72]]
| [[73ed7|73]]
| [[74ed7|74]]
| [[75ed7|75]]
| [[76ed7|76]]
| [[77ed7|77]]
| [[78ed7|78]]
| [[79ed7|79]]
|-
| [[80ed7|80]]
| [[81ed7|81]]
| [[82ed7|82]]
| [[83ed7|83]]
| [[84ed7|84]]
| [[85ed7|85]]
| [[86ed7|86]]
| [[87ed7|87]]
| [[88ed7|88]]
| [[89ed7|89]]
|-
| [[90ed7|90]]
| [[91ed7|91]]
| [[92ed7|92]]
| [[93ed7|93]]
| [[94ed7|94]]
| [[95ed7|95]]
| [[96ed7|96]]
| [[97ed7|97]]
| [[98ed7|98]]
| [[99ed7|99]]
|}
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style=white-space:nowrap | 100…199
| [[100ed7|100]]
| [[101ed7|101]]
| [[102ed7|102]]
| [[103ed7|103]]
| [[104ed7|104]]
| [[105ed7|105]]
| [[106ed7|106]]
| [[107ed7|107]]
| [[108ed7|108]]
| [[109ed7|109]]
|-
| [[110ed7|110]]
| [[111ed7|111]]
| [[112ed7|112]]
| [[113ed7|113]]
| [[114ed7|114]]
| [[115ed7|115]]
| [[116ed7|116]]
| [[117ed7|117]]
| [[118ed7|118]]
| [[119ed7|119]]
|-
| [[120ed7|120]]
| [[121ed7|121]]
| [[122ed7|122]]
| [[123ed7|123]]
| [[124ed7|124]]
| [[125ed7|125]]
| [[126ed7|126]]
| [[127ed7|127]]
| [[128ed7|128]]
| [[129ed7|129]]
|-
| [[130ed7|130]]
| [[131ed7|131]]
| [[132ed7|132]]
| [[133ed7|133]]
| [[134ed7|134]]
| [[135ed7|135]]
| [[136ed7|136]]
| [[137ed7|137]]
| [[138ed7|138]]
| [[139ed7|139]]
|-
| [[140ed7|140]]
| [[141ed7|141]]
| [[142ed7|142]]
| [[143ed7|143]]
| [[144ed7|144]]
| [[145ed7|145]]
| [[146ed7|146]]
| [[147ed7|147]]
| [[148ed7|148]]
| [[149ed7|149]]
|-
| [[150ed7|150]]
| [[151ed7|151]]
| [[152ed7|152]]
| [[153ed7|153]]
| [[154ed7|154]]
| [[155ed7|155]]
| [[156ed7|156]]
| [[157ed7|157]]
| [[158ed7|158]]
| [[159ed7|159]]
|-
| [[160ed7|160]]
| [[161ed7|161]]
| [[162ed7|162]]
| [[163ed7|163]]
| [[164ed7|164]]
| [[165ed7|165]]
| [[166ed7|166]]
| [[167ed7|167]]
| [[168ed7|168]]
| [[169ed7|169]]
|-
| [[170ed7|170]]
| [[171ed7|171]]
| [[172ed7|172]]
| [[173ed7|173]]
| [[174ed7|174]]
| [[175ed7|175]]
| [[176ed7|176]]
| [[177ed7|177]]
| [[178ed7|178]]
| [[179ed7|179]]
|-
| [[180ed7|180]]
| [[181ed7|181]]
| [[182ed7|182]]
| [[183ed7|183]]
| [[184ed7|184]]
| [[185ed7|185]]
| [[186ed7|186]]
| [[187ed7|187]]
| [[188ed7|188]]
| [[189ed7|189]]
|-
| [[190ed7|190]]
| [[191ed7|191]]
| [[192ed7|192]]
| [[193ed7|193]]
| [[194ed7|194]]
| [[195ed7|195]]
| [[196ed7|196]]
| [[197ed7|197]]
| [[198ed7|198]]
| [[199ed7|199]]
|}

; 200 and above
* [[480ed7]]

[[Category:Ed7's| ]]
<!-- main article -->
{{todo|inline=1|cleanup|explain edonoi|text=Most people do not think 7/1 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.}}